| ||  MATH 412
Partial Differential Equations
Penn State University
Tu / Th 9:45 - 11 AM
Contact info: 322 McAllister Building, telephone: 865-2491, email: belmonte.AT.math.psu.edu
Office hours: Mon 2:30--4, Tues 3--4, Wed 11--12, or by appointment.
Class location: 014 Henderson Bldg                                                     Registrar Schedule Number: 920407
Prerequisites: Math 230 or 231 and Math 250 or 251. For more information, please contact the instructor.Course Text (required):
We live in a three-dimensional world defined by the passage of time, so it should not surprise us that many of the equations describing that world are partial differential equations (PDEs). The purpose of this course is to introduce you to these important equations - their origins, their applications, in some cases how to solve them, or at least what can be said about them mathematically. We will develop the mathematical theory of PDEs, and systematically explore several of the most well-known cases. One theme of the course will be the relationship between the mathematical properties of the equations and their physical basis; in many instances physical intuition corresponds surprisingly well to the mathematical aspects of the solution to the PDE.
There is not one technique for solving PDEs, but many - depending for instance if it is more like a wave equation (hyperbolic) or a heat equation (parabolic).
Many of the topics we will cover can be classified under what the text calls ``flows, vibrations, and diffusions". In addition we will cover expansions in orthogonal functions, eigenvalue theory, some aspects of functional analysis, the use of Fourier and Laplace transforms to solve PDEs, and the notion of weak derivatives.
The structure of the course will follow the main text (Strauss), including most of Chapters 1-7 and 9-12, with some selections from Chapters 13-14 depending on student interests.
Midterm I:   Thursday, February 28th (in class).
Midterm II:   Thursday, April 17th (in class).
Final Exam:   Tuesday, May 6th: 6:50-8:40 PM - 124 Agricultural Engineering - MAP of campus